(4/x-4)-(4/2x-8)=6

Solution for (4/x-4)-(4/2x-8)=6 equation:

(4/x-4)-(4/2x-8)=6

We move all terms to the left:

(4/x-4)-(4/2x-8)-(6)=0


Domain of the equation: x-4)!=0

x∈R



Domain of the equation: 2x-8)!=0

x∈R


We get rid of parentheses

4/x-4/2x-4+8-6=0

We calculate fractions


8x/2x^2+(-4x)/2x^2-4+8-6=0

We add all the numbers together, and all the variables

8x/2x^2+(-4x)/2x^2-2=0

We multiply all the terms by the denominator


8x+(-4x)-2*2x^2=0

Wy multiply elements

-4x^2+8x+(-4x)=0

We get rid of parentheses

-4x^2+8x-4x=0

We add all the numbers together, and all the variables

-4x^2+4x=0

a = -4; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-4)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-4}=\frac{0}{-8}
=0
$